It was one of those experiences that none of them could ever forget: a sullen Natalie Wood kept to herself, a perfectionist Jerome Robbins was fired for blowing the budget and an inspired Montgomery Clift got the whole thing rolling.

Just play it cool, boys and girls: The movie version of “West Side Story” is turning 40.

“Great ideas can be expressed in a sentence,” said Russ Tamblyn, 66, who played Riff, one of the Jets: “Romeo and Juliet with gangs set in New York.”

Based on the Broadway musical, the Manhattan-based, finger-snappin’ flick wowed critics and fans in 1961, thanks to Robbins’ jazz choreography, Leonard Bernstein’s music, Stephen Sondheim’s lyrics and a cast blazing with enthusiasm.

“This was a movie with a knife-sharp edge,” said actress Rita Moreno (Anita), 69, now a grandmother of two.

The modern retelling of Romeo and Juliet as a teenage turf war eventually snatched 10 Academy Awards, including best supporting nods for Moreno and co-star George Chakiris (Bernardo).

To celebrate the anniversary, cast members, producers and co-director Robert Wise are reuniting for a party and sold-out screening – sponsored by Turner Classic Movies and Time Warner Cable of New York City – at Radio City Music Hall this Saturday.

But before that event, some affiliated with the movie spoke with The Post and set the clock back.

Like the windowpanes in Maria’s room, the history of “West Side Story” the movie is a colorful one.

The mischievous cast bonded, while the movie went massively over budget and massively behind schedule. That was mostly due to choreographer and co-director Robbins, a stickler for details, cast members said.

“That’s one of the problems we had – making take after take after take,” said Wise, 87, who shared the Oscar honors for Best Director with Robbins and also worked as a film editor on “Citizen Kane.”

Robbins would try different versions of dance numbers, shooting scenes over and over again, Wise said. An example: the opening number, the first and only segment lensed in New York.

The West Side meeting between rival gangs – filmed where Lincoln Center now stands – “went weeks,” said Tamblyn.

Tamblyn remembered dancing with others down an entire city block. After the scene ended, Wise was ready to move on, said Tamblyn.

But Robbins – who once told Tamblyn he got the “musical about gangs” idea from Clift – felt differently.

“‘I want to see it again and I want to see it on the other foot,'” Tamblyn remembers Robbins saying. “It was kind of annoying,” said Tamblyn, whose fingers were sore from snapping “all day long.”

Months into the half-year shoot, the film’s producers had had enough. Robbins was canned.

“Jerry wanted everything perfect. That’s not possible. It eventually led to him being dismissed from the movie,” said Moreno, who was heartbroken by the decision.

The cast went on – as they had all along.

“We were mighty. We had such huge presence,” Moreno said.

Gang members battled with each other good-naturedly between takes. Dancers smoked cigarettes with one another during breaks. Wise, who owned two racehorses, threw a big cast party on the Hollywood set whenever one of his horses won.

But Robbins did insist that rival Jets and Sharks not get too close. The Sharks put on leather wristbands as part of their costumes. The Jets had their own clubhouse. The Sharks hung a banner on a fire escape. The Jets took it down.

“Jerry insisted that we stay apart while we were working,” said Tamblyn.

Said Moreno: “It was like a playground, only with grown kids.”

But sometimes they teamed up to pull a gag.

“One time, the two gangs got together and they picked up the Volkswagen of our assistant director,” said Moreno. “They put it somewhere else on the lot. He went mad that evening trying to find the damn car.”

All the cast seemed to be having a good time, but there was one exception: Natalie Wood, whose singing voice had to be dubbed by Marni Nixon. (Nixon was also the pipes behind Audrey Hepburn in “My Fair Lady” and Deborah Kerr in “The King and I.”)

“She said she wasn’t right for the part,” said Moreno. “And she wasn’t. She wasn’t friendly. She wasn’t rude. She just was aloof.”

Today, Wise sticks by the decision to cast Wood. “I thought she was fine with the part,” he said.

Trivia lovers will note that Warren Beatty was the first choice to play Tony – until Wise saw the audition tapes for “Splendor in the Grass.” What he witnessed was Beatty being eclipsed by his fresh-faced co-star, Wood.

“We forgot immediately about Warren,” said Wise. “We said, ‘That’s our Maria right there.’ Maybe we should have taken them both,” he joked.

Those involved said they were looking forward to coming back to New York to celebrate the anniversary and honor the victims of the World Trade Center tragedy.

In an eerie coincidence, “West Side Story” opens up with a shot of lower Manhattan – less than a decade before the Towers were built.

“After Sept. 11, you feel that it’s especially important to be with people and to enjoy fine art and music like this together,” said Nixon.